# ORMC Meetings • 2020-2021 Academic Year

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### For meetings prior to Fall 2020, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 TrainingBeginners 1ABeginners 1BBeginners 1CBeginners 2A
Beginners 2BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
 10/11/2020 We will start the year with a wide variety of competition style problems.Handouts: Competition Problems [Show less] 10/18/2020 We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.Handouts: Gaussian Integers I [Show less] 10/25/2020 We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares.Handouts: Gaussian Integers II [Show less] 11/1/2020 We will study the limitations of polynomials as prime generating functions.Handouts: Prime Generating Functions I [Show less] 11/8/2020 We will study recursive formulas for generating primes.Handouts: Prime Generating Functions II [Show less] 11/15/2020 We introduce some classic algorithms and the notion of runtime.Handouts: Intro to Algorithms [Show less] 11/22/2020 Following the introduction to algorithms, we are able to discuss the nuances of the P vs. NP problem.Handouts: P vs NP [Show less] 12/6/2020 We prove the Fundamental Theorem of Algebra with a focus on graphing.Handouts: Fundamental Theorem of Algebra [Show less] 12/13/2020 The students battle it out in a full class Kahoot competition. [Show less] 1/10/2021 Handouts: Competition Problems [Show less] 1/17/2021 We will attempt to determine when a given graph is planar, culminating in Kuratowski's Theorem.Handouts: Planar Graphs [Show less] 1/24/2021 We will explore many interesting results about graph coloring.Handouts: Graph Coloring [Show less] 1/31/2021 We will finish the study of graph coloring and introduce basic ideas in Ramsey Theory.Handouts: Graph Coloring [Show less] 2/7/2021 Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions.Handouts: Continued Fractions [Show less] 2/21/2021 We introduce the taxicab metric, a new way of measuring distance in Euclidean space. We will study its properties and figure out how it relates to the Euclidean metric.Handouts: Taxicab Geometry [Show less] 2/28/2021 We generalize different notions of distances, as motivated by the taxicab distance, into something called a metric space. We then discuss convergence of sequences in metric spaces.Handouts: Handout [Show less] 3/7/2021 In economics, the Gini index is a measure intended to represent income inequality. We will take a mathematical approach to the study of the Gini index.Handouts: Gini Index [Show less] 3/14/2021 Handouts: Competition Problems [Show less] 4/4/2021 Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.Handouts: handout [Show less] 4/11/2021 Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits. [Show less] 4/18/2021 We will show that certain regions of Euclidean space must contain integer lattice points.Handouts: Lattices [Show less] 4/25/2021 We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.Handouts: Smart Codes [Show less] 5/2/2021 We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.Handouts: Smart Codes [Show less] 5/9/2021 Handouts: Competition Problems [Show less] 5/16/2021 We will define what it means for a sequence to converge in different metric spaces. We will explore many different examples like convergence with the taxicab metric or the discrete metric.Handouts: Convergence in Metric Spaces I [Show less] 5/23/2021 We define the notion of a continuous function using limits in arbitrary metric spaces. We apply the Intermediate Value Theorem to a range of functions on the real line.Handouts: Convergence in Metric Spaces II [Show less] 6/6/2021 Handouts: Competition Problems [Show less]